Flux and nonconducting shells. A charged particle is suspended at the center of
ID: 1526326 • Letter: F
Question
Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure shows a cross section. Figure gives the net flux Phi through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. (The vertical axis is marked in increments of 2.0 times 10^5 N middot m^2/C with phi_s = 1.0 times 10^6 N middot m^2/C) What is the charge of the central particle? What is the net charge of shell A? What is the net charge of shell B?Explanation / Answer
a) flux through A is phi_s = 0.4*10^6 N-m^2/C
phi_s = q_inside/eo = 0.4*10^6 N-m^2/C
eo is the permittivity of free space
q_inside/(8.85*10^-12) = 0.4*10^6
q_inside = 8.85*10^-6*0.4 C = +3.54 uC
2) flux through shell A is
phi = q_inside/eo = -0.8*10^6
q_inside = -0.8*8.85*10^-6 = -7.08*10^-6 = -7.08 uC
3) net charge of shell is q
net fluX through B is 1.2*10^6 N-m^2/C
q/eo = 1.2*10^6
q = 8.85*10^-12*1.2*10^-6 = 10.62*10^-6 C = +10.62 uC